Light micrographs of the whirligig beetle.

<p>(A) Dorsal view of the beetle, demonstrating the overall shape. (B) Ventral view of the beetle showing the fore, middle and hind legs. (C&D) Micrographs of dissected middle right (C) and left (D) legs. (E&F) Micrographs of dissected hind right (E) and left (F) legs. Measurements of leg length (<i>L_h</i> and <i>L_m</i>) and area (<i>S_h−</i> and <i>S_m−</i>) were made from micrographs of dissected legs. The scale bars are 1 mm.</p

Experimental Studies and Dynamics Modeling Analysis of the Swimming and Diving of Whirligig Beetles (<i>Coleoptera:</i> <i>Gyrinidae</i>)

<div><p>Whirligig beetles (<i>Coleoptera</i>, <i>Gyrinidae</i>) can fly through the air, swiftly swim on the surface of water, and quickly dive across the air-water interface. The propulsive efficiency of the species is believed to be one of the highest measured for a thrust generating apparatus within the animal kingdom. The goals of this research were to understand the distinctive biological mechanisms that allow the beetles to swim and dive, while searching for potential bio-inspired robotics applications. Through static and dynamic measurements obtained using a combination of microscopy and high-speed imaging, parameters associated with the morphology and beating kinematics of the whirligig beetle's legs in swimming and diving were obtained. Using data obtained from these experiments, dynamics models of both swimming and diving were developed. Through analysis of simulations conducted using these models it was possible to determine several key principles associated with the swimming and diving processes. First, we determined that curved swimming trajectories were more energy efficient than linear trajectories, which explains why they are more often observed in nature. Second, we concluded that the hind legs were able to propel the beetle farther than the middle legs, and also that the hind legs were able to generate a larger angular velocity than the middle legs. However, analysis of circular swimming trajectories showed that the middle legs were important in maintaining stable trajectories, and thus were necessary for steering. Finally, we discovered that in order for the beetle to transition from swimming to diving, the legs must change the plane in which they beat, which provides the force required to alter the tilt angle of the body necessary to break the surface tension of water. We have further examined how the principles learned from this study may be applied to the design of bio-inspired swimming/diving robots.</p></div

The sequence of one hind leg stroke.

<p>In frames 1–5, only the hind leg is visible, with the middle leg emerging in frame 6. In frames 6–10 it is possible to observe the beating of both legs. During the course of one leg stroke, the effective area of the legs decreases in the horizontal plane, indicating that the effective area for forward propelling increases.</p

Analysis of circling trajectories.

<p>Analysis of circling trajectories.</p

Dendritic stratification patterns of OFF bipolar cells.

<p><b>A-P:</b> Maximum intensity projections of confocal image stacks from vertical cryosections of wild-type (A-H) and <i>Nrl</i>^-/- (I-P) mice double-labeled with ribbon markers bassoon (A) or CtBP2 (all other). OFF bipolar cells were labeled with antibodies against NK3R (types 1 and 2; A,B,I,J), HCN4 (type 3a; C,D,K,L), PKARIIβ (type 3b; E,F,M,N), and calsenilin (Csen, type 4; G,H,O,P). Dashed lines in O indicate the inner and outer border of the CtBP2 labeled area (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0173455#pone.0173455.g002" target="_blank">Fig 2A</a> for more details). Scale bar = 10 μm for all panels.</p

Time-lapse images of the diving process.

<p>This image shows the complete diving process, from the 83 ms pre-diving to the 89 ms diving process. To illustrate the diving motion, images captured every 17 ms are overlaid onto each other to show the complete diving motion.</p

Results from the diving simulations.

<p>Simulation results of diving with different initial conditions. The initial values of forward speed (0.17 m/s), angular velocity of the body (−333°/s), tilt angle of the body (7°), striking speed of the hind legs (0.18 m/s), and striking speed of the middle legs (0.14 m/s), were varied ±30% to determine the effect on the diving trajectory. Each of these terms was varied ±30%, with the other terms held constant, to determine their effects on the overall trajectory. The values generated the closest diving trajectory as observed in the experimental studies was with an initial speed of 0.17 m/s, angular velocity of −333°/s, tilt angle of −7°, hind leg speed of 0.18 m/s, and middle leg speed of 0.14 m/s.</p

Circling trajectories from swimming simulations.

<p>The circular trajectories obtained from the swimming simulations are illustrated above. Based on the simulations, only three beating patterns stabilized to form a consistent circular trajectory, the middle right leg only (<i>m_r</i>), the middle right followed by the hind right (<i>m_r</i>, <i>h_r</i>), and the middle right followed by the simultaneous beating of the hind legs (<i>m_r</i>, <i>h_r</i>+<i>h_l</i>). The other beating patterns analyzed produced unstable trajectories, resulting in trajectories not observed in nature. Numerical analysis of the circular swimming trajectories is shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002792#pcbi-1002792-t005" target="_blank"><b>Table 5</b></a>.</p

Swimming parameters obtained from high-speed video analysis.

<p>Swimming parameters obtained from high-speed video analysis.</p

Parameters obtained from micrographs.

<p>Parameters obtained from micrographs.</p